A correction to my work: "A new determination of molecular dimensions" by A. Einstein. A few weeks ago, Mr. Bacelin, who conducted an experimental investigation on the viscosity of suspensions at the request of Mr. Perrin, informed me by letter that the viscosity coefficient of suspensions was significantly larger than predicted by the formula developed in § 2 of my work. I therefore asked Mr. Hopf to check my calculations, and he found a computational error that significantly distorted the result. I now correct this error.
On page 296 of the mentioned paper, expressions for the stress components $X_y$ and $X_z$ are incorrectly derived due to a mistake in differentiating the velocity components $u, v, w$. The corrected expressions are:
$$ X_{x}=-2k A+10k P^{3}\quad\frac{A\xi^{3}}{\varrho^{5}}\quad-25k P^{3}\quad\frac{M\xi^{2}}{\varrho^{7}}\quad, $$
$$ X_{y}=\quad5\quad h\quad P^{3}\quad\underset{\varrho^{5}}{\overset{(A+B)\xi\eta}{\sim}}-25\quad h\quad P^{3}\quad\underset{\varrho^{7}}{\overset{M\xi\eta}{\sim}}\quad, $$
$$ X_{z}=\quad5k P^{3}\stackrel{(A+C)}{\underset{\varrho^{5}}{\underbrace{\quad\xi\xi\quad}}}-25k P^{3}\stackrel{M\xi\xi}{\underset{\varrho^{7}}{\underbrace{\quad\xi\xi\quad}}}, $$
where $M = A\xi^{2} + B\eta^{2} + C\zeta^{2}$. Calculating the energy transferred per unit time to the liquid contained in a sphere of radius R by pressure forces, one obtains instead of equation (7) on page 296:
$$ W=2\;\delta^{2}\;k\left(V+\mathrm{~\frac{1}{2}~}\Phi\right). $$
Using this corrected equation, one obtains instead of the equation $k^{*}=k(1+\varphi)$ developed in § 2 the equation $k^{*}=k(1+2,5\varphi)$. The viscosity coefficient $k^{*}$ of the suspension is thus 2.5 times more strongly influenced by the total volume $\varphi$ of the suspended spheres per unit volume than previously found. Based on the corrected formula, the volume of 1 g of dissolved sugar in water is 0.98 cm³ instead of 2A correction to my work: "A new determination of molecular dimensions" by A. Einstein. A few weeks ago, Mr. Bacelin, who conducted an experimental investigation on the viscosity of suspensions at the request of Mr. Perrin, informed me by letter that the viscosity coefficient of suspensions was significantly larger than predicted by the formula developed in § 2 of my work. I therefore asked Mr. Hopf to check my calculations, and he found a computational error that significantly distorted the result. I now correct this error.
On page 296 of the mentioned paper, expressions for the stress components $X_y$ and $X_z$ are incorrectly derived due to a mistake in differentiating the velocity components $u, v, w$. The corrected expressions are:
$$ X_{x}=-2k A+10k P^{3}\quad\frac{A\xi^{3}}{\varrho^{5}}\quad-25k P^{3}\quad\frac{M\xi^{2}}{\varrho^{7}}\quad, $$
$$ X_{y}=\quad5\quad h\quad P^{3}\quad\underset{\varrho^{5}}{\overset{(A+B)\xi\eta}{\sim}}-25\quad h\quad P^{3}\quad\underset{\varrho^{7}}{\overset{M\xi\eta}{\sim}}\quad, $$
$$ X_{z}=\quad5k P^{3}\stackrel{(A+C)}{\underset{\varrho^{5}}{\underbrace{\quad\xi\xi\quad}}}-25k P^{3}\stackrel{M\xi\xi}{\underset{\varrho^{7}}{\underbrace{\quad\xi\xi\quad}}}, $$
where $M = A\xi^{2} + B\eta^{2} + C\zeta^{2}$. Calculating the energy transferred per unit time to the liquid contained in a sphere of radius R by pressure forces, one obtains instead of equation (7) on page 296:
$$ W=2\;\delta^{2}\;k\left(V+\mathrm{~\frac{1}{2}~}\Phi\right). $$
Using this corrected equation, one obtains instead of the equation $k^{*}=k(1+\varphi)$ developed in § 2 the equation $k^{*}=k(1+2,5\varphi)$. The viscosity coefficient $k^{*}$ of the suspension is thus 2.5 times more strongly influenced by the total volume $\varphi$ of the suspended spheres per unit volume than previously found. Based on the corrected formula, the volume of 1 g of dissolved sugar in water is 0.98 cm³ instead of 2